I’ve had a similar problem before. I found that plugins like WordFence conflict with multisite, but as you’ve said this has been checked.

I’d try checking the wp-config. Here is a link to a base copy of mine. Alter it to fit your needs and try that: http://pastebin.com/m4dqDGBC

If these don’t work, this may be a bit much for this forum, and may need someone to diagnose it by logging in. If you create a job on jobs.wordpress.net and reference Huddersfield Hosting in the title, I’ll fix for free, because I know how frustrating this is.